11.3 Day 4 - Homework 1. After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12 minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6 minutes per day. How many weeks will it be before you are up to jogging 60 minutes per day? 2. Would you rather have $1,000,000 and a brand new BMW or 1¢ today, 2¢ tomorrow, 4¢ on day 3, 8¢ on day 4, 16¢ on day 5, and so on, for 30 days? Explain.

3. The first year a toy manufacturer introduces a new toy, its sale total $495,000. The company expects its sales to drop 10% each succeeding year.

a. Find the total expected sales in the first 6 years. b. Find the total expected sales if the company offers the toy for sale as long as anyone buys it (assume forever).

4. (#84 from book) The first swing of a bob on a pendulum is 10 inches. If on each subsequent swing it travels .9 as far as on the preceding swing, how far will the bob travel before coming to rest?

5. (#94 from book) The notes on a piano, as measured in cycles per second, form a geometric sequence:

a. If A is 400 cycles per second, and A' 12 notes higher, is 800 cycles per second, find the constant ratio.

b. Find the cycles per second for C, three notes higher than A.

6. (#83 from book) A rotating flywheel coming to rest rotates 300 revolutions the first minute. If in each subsequent minute it rotates two-thirds as many times as in the preceding minute, how many revolutions will the wheel make before coming to rest? 7. A new factory in a small town has an annual payroll of $6 million. It is expected that 60% of this money will be spent in the town by factory personnel. The people in the town who receive this money are expected to spend 60% of what they receive in the town and so on. What is the TOTAL of all this spending (which is called total economic impact), on the town each year? 8. Suppose that you are offered a job with a starting annual salary of $40,000 and an annual increase of 4% of the current salary.

a. Write the explicit formula for the sequence representing your salary over ‘n’ years.

b. Write the summation notation for the series showing your first 6 years of the job. Find the value of this series and explain its meaning.